Algebraic geometry is the hottest field of mathematics today, and more than half of the mathematicians devote themselves to this field, and Shen Qi is not the only one who is interested in completing the Langlands program or the Hodge conjecture.

The team of Wu Baozhu of the University of Chicago and the team of La Fogue of the École Supérieure de Paris are at the forefront of the world in terms of the Langlands program, and the mathematical community generally believes that whoever can be the first to prove and perfect the Langlands program will realize the great unification that mathematicians dream of.

The Langlands program is quite difficult, Wu Baozhu and Laverge have each studied it for ten or twenty years, and so far they have only proved a lemma and an inference in the Langlands program.

It is with this lemma and this inference that Wu Baozhu and Lafoute won the Fields Medal respectively.

The Langlands Program builds a system, and the Hodge conjecture is the most complex case.

Since the Hodge conjecture was proposed in 1950, mathematicians have been trying to prove it.

Two years ago, Peter Schulz's team at the University of Bonn in Germany demonstrated a coincidence that a nonsingular projective complex algebraic cluster can partially characterize cohomology classes in algebra.

Schultz, who missed out on the Philippine Prize two years ago, has been attacking Hodge's conjecture with all his firepower for the past two years, and his latest paper published in Mathematical Inventions has made Shen Qi slightly nervous.

"Schultz's latest research has proved the similarity of the elements in the upper cohomology class, which I have to say is a very beautiful proof. Shen Qi repeatedly studied Schultz's new paper, and he felt that Schultz was doing the right thing on the right path: "I must not let Schultz or anyone else prove the Hodge conjecture before me, and completing the proof of the Hodge conjecture is one of my must-choose tasks." ”

However, mathematics is not a confrontational type of combat competition, and the trade-off rule does not apply to mathematics.

The only effective way to beat your opponent in math is to do it faster and better than your opponent.

Mathematics is more like a sprint, one track for one person, you don't have to care too much about whether the opponent is running fast or slow, what Shen Qi has to do is to run the fastest speed in the whole field on his own track.

At the end of the Christmas break, Lei Yu and Ralph returned to campus for their second semester as PhD students.

"Boys, Schultz of the University of Bonn is about to catch up with us, yes, he and his team are also tackling the Hodge conjecture! We must be clear that the Hodge conjecture is not our patent, and anyone has the right to have ideas about it and take practical action! Obviously, the teams competing with us on the Hodge conjecture are far superior to the Riemann conjecture in quantity and quality, after all, there are only a few internationally renowned number theory teams, and the algebraic geometry team ...... I can't count them!" Shen Qi and his two doctoral students moved from the outdoors to his office.

In this special period, it is necessary to keep it secret, and it is best not to let anyone else see even one of the formulas in the semi-finished product.

Although the vast majority of people in the world cannot understand Hodge's conjecture and cannot understand the verification ideas of Shen Qi's team, they have mobile phones, and there is a camera function in them.

Peter Schultz, who, two years ago made a corollary of a partial description of an algebraic cohomology class on a nonsingular projective complex algebraic cluster, and has just proved the similarity of the elements in the cohomology class, has been ...... in the proof of Hodge's conjecture Oh no, it's about to catch up with us. Ralph's brow furrowed, and any mathematician has a heart for "first proof".

"Ralph, are you timid, are you afraid?" asked Shen Qi.

"No, we will not back down, and there is no way back. ”

"Good. Shen Qi expressed his satisfaction, he was very concerned about Ralph's mentality and state.

Ralph is the only American in the whole team, and his undergraduate, master's, and doctoral students all studied at Princeton.

"This Schultz is two brushes, it is said that he is Sister Mary's ex-husband?" Yu Lei's thinking is more divergent, he is good at starting from multiple angles, comprehensively and objectively analyzing and solving problems.

Shen Qi nodded: "Yes, this German madman loves mathematics more than his wife." ”

"I studied mathematics until I didn't even want a wife, and if I wasn't afraid of dying, I was afraid that I wouldn't want a wife...... Schulz, he's our toughest opponent. Yu Lei felt a chill, and he said: "Professor Shen, I think you are more humane, so you won the Fields Medal, but Schultz did not win the award." ”

"Remember, we don't make friends with men who don't love their wives. Okay, let's get down to business, I hope your paper will be published within this semester, at least pre-recorded on arVix, and we need to show what we can do. Shen Qi put forward specific requirements for the two doctoral students, and the next step was the technical guidance session.

Shen Qi's thinking has something in common with Schultz, and there are also unique highlights.

Shen Qi inevitably has to intersect with Schultz in the part of the same tonality, it is all such a routine, you are allowed to use it or not, I am not allowed to use it.

Schultz is a master of playing routines, and to be more exciting than Schultz, Shen Qi needs to play some anti-routines, and the most important thing is how to reverse deduce that non-singular projective complex algebraic clusters are a special type of complex manifolds.

The reverse derivation lasted for more than half a year, and the details were in charge of Lei and Ralph, and Shen Qi grasped the direction.

In the proof of Hodge's conjecture, to put it in layman's terms, Schultz adopted the method of forward and strong push, and his core logic was based on pure algebraic geometry methods, and achieved good results.

Shen Qi adopts a combination of forward and backward push, and his core logic is based on algebraic geometry, mathematical analysis, and topology, and the system framework is more perfect, but its verification process is also more brain-burning and complex, which requires a large team of basic theories to complete this arduous task with him.

Yu Lei and Ralph worked under Shen Qi's nose, Shen Qi was very aware of the progress of the project that the two doctoral students were responsible for, and he thought that he had supervised quite well and was a qualified doctoral supervisor.

Shen Qi is also very concerned about the progress of the project that Lu Guozhen and Director Wu are responsible for on the Chinese side, and they keep in touch and communicate with each other.

"Director Lu, how is the progress of the mathematical analysis section over there?" asked Shen Qi during the video call.

"It's going well, you can relax! My 973 project is an annual major project in the hospital, and the dean has sent me two more elites, and the morale of our team is high, and the situation is very good!" Lu Guozhen in the video screen is full of red light, and the old man is talking about juvenile madness.

Shen Qi was greatly encouraged: "Great, Director Lu is really powerful! We don't need to communicate the specific technical details in the video call, and the communication is not clear, Director Lu, you give me a thorough understanding, when can we have the first joint manuscript?"

Lu Guozhen: "It is expected to be in July." ”

Shen Qi: "Okay, it's about the same time as I envisioned, and I'm looking forward to your research results!" ()

Please remember that the first domain name of this book is:. Mobile version reading URL: